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Evaluate the left hand side to find the value of a in the equation in simplest form. (x^(2))/(x^((1)/(5)))=x^(a) Answer:

Evaluate the left hand side to find the value of a a in the equation in simplest form.\newlinex2x15=xa \frac{x^{2}}{x^{\frac{1}{5}}}=x^{a} \newlineAnswer:

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Full solution

Q. Evaluate the left hand side to find the value of a a in the equation in simplest form.\newlinex2x15=xa \frac{x^{2}}{x^{\frac{1}{5}}}=x^{a} \newlineAnswer:
  1. Simplify using exponent property: To simplify the expression on the left-hand side, we use the property of exponents that states when dividing like bases, we subtract the exponents: xm/xn=x(m−n)x^m / x^n = x^{(m-n)}.\newlineSo, (x2)/(x(1/5))=x(2−1/5)(x^{2})/(x^{(1/5)}) = x^{(2 - 1/5)}.
  2. Perform exponent subtraction: Now we need to perform the subtraction in the exponent: 2−152 - \frac{1}{5}. To subtract these, we can write 22 as a fraction with a common denominator of 55: (105)−(15)=(95)(\frac{10}{5}) - (\frac{1}{5}) = (\frac{9}{5}).
  3. Final simplified expression: We have simplified the left-hand side to x95x^{\frac{9}{5}}. Therefore, the value of 'aa' in the equation x2x15=xa\frac{x^{2}}{x^{\frac{1}{5}}}=x^{a} is 95\frac{9}{5}.

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